# An Efficient Parallel Algorithm for Computing Bicompatible Elimination Ordering (BCO) of Proper Interval Graphs

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## Abstract

In this paper, we first show how a certein ordering of vertices, called *bicompatible elimination ordering* (BCO), of a proper interval graph (PIG) can be used to solve optimally the following problems: finding Hamiltonian cycle in a Hamiltonian PIG, the set of articulation points and bridges, and the single source or all pair shortest paths. We then propose an NC parallel algorithm (i.e., polylogarithmic-time employing a polynomial number of processors) to compute a BCO of a proper interval graph.

## Keywords

Leaf Node Parallel Algorithm Hamiltonian Cycle Interval Graph Chordal Graph
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